login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003592 Numbers of the form 2^i*5^j with i, j >= 0. 48
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1000, 1024, 1250, 1280, 1600, 2000, 2048, 2500, 2560, 3125, 3200, 4000, 4096, 5000, 5120, 6250, 6400, 8000, 8192, 10000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

These are the natural numbers whose reciprocals are terminating decimals. - David Wasserman, Feb 26 2002

A132726(a(n),k)=0 for k<=a(n); A051626(a(n))=0; A132740(a(n))=1; A132741(a(n))=a(n). - Reinhard Zumkeller, Aug 27 2007

Where record values greater than 1 occur in A165706: A165707(n)=A165706(a(n)). [Reinhard Zumkeller, Sep 26 2009]

Also numbers that are divisible by neither 10k-7, 10k-3, 10k-1 nor 10k+1, for all k > 0. [Robert G. Wilson v, Oct 26 2010]

A204455(5*a(n)) = 5, and only for these numbers. - Wolfdieter Lang, Feb 04 2012

Since p=2 and q=5 are coprime, sum_{n>=1} 1/a(n) = sum_{i>=0} sum_{j>=0} 1/p^i * 1/q^j = sum_{i>=0} 1/p^i q/(q-1) = p*q/((p-1)*(q-1)) = 2*5/(1*4) = 2.5. - Franklin T. Adams-Watters, Jul 07 2014

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Regular Number

Eric Weisstein's World of Mathematics, Decimal Expansion

MAPLE

isA003592 := proc(n)

      if n = 1 then

        true;

    else

        return (numtheory[factorset](n) minus {2, 5} = {} );

    end if;

end proc:

A003592 := proc(n)

     option remember;

     if n = 1 then

        1;

    else

        for a from procname(n-1)+1 do

            if isA003592(a) then

                return a;

            end if;

        end do:

    end if;

end proc: # R. J. Mathar, Jul 16 2012

MATHEMATICA

fQ[n_] := PowerMod[10, n, n] == 0; Select[ Range@ 10000, fQ] (* Robert G. Wilson v, Jan 12 2012 *)

fQ[n_] := Union[ MemberQ[{1, 3, 7, 9}, # ] & /@ Union@ Mod[ Rest@ Divisors@ n, 10]] == {False}; fQ[1] = True; Select[ Range@ 10000, fQ] (* Robert G. Wilson v, Oct 26 2010 *)

mx = 14; Sort@ Flatten@ Table[2^i*5^j, {i, 0, mx}, {j, 0, Log[5, 2^(mx - i)]}] (* Or *)

Union@ Flatten@ NestList[{2#, 4#, 5#} &, 1, 7] (* Robert G. Wilson v, Apr 16 2011 *)

PROG

(PARI) list(lim)=my(v=List(), N); for(n=0, log(lim+.5)\log(5), N=5^n; while(N<=lim, listput(v, N); N<<=1)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jun 28 2011

(Sage)

def isA003592(n) :

    return [] == filter(lambda d: d != 2 and d != 5, prime_divisors(n))

@CachedFunction

def A003592(n) :

    if n == 1 : return 1

    k = A003592(n-1) + 1

    while not isA003592(k) : k += 1

    return k

[A003592(n) for n in (1..48)]  # Peter Luschny, Jul 20 2012

(MAGMA) [n: n in [1..10000] | PrimeDivisors(n) subset [2, 5]]; // Bruno Berselli, Sep 24 2012

CROSSREFS

Complement of A085837. Cf. A094958.

Sequence in context: A181666 A067943 A067937 * A192716 A159765 A018653

Adjacent sequences:  A003589 A003590 A003591 * A003593 A003594 A003595

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 19 18:23 EST 2014. Contains 252239 sequences.